Reflections on the Covariance of Modified Teleparallel Theories of Gravity
Abstract
:1. Introduction
2. Teleparallel Gravity
2.1. Geometric Foundations of General Relativity
2.2. The Teleparallel Equivalent of General Relativity
3. Modified Teleparallel Gravities
4. Covariance in Modified Teleparallel Gravity
5. Remnant Symmetries and The Lorentz Group
- Why, for a given spacetime , there are certain proper tetrads , and others that definitely do not lead to a consistent set of equations of motion for a function other than the one corresponding to GR?
- Once the above point was established, is there any way of counting the number of proper tetrads, and some systematic procedure in order to obtain them?
- What is the physical meaning of the proper tetrads?
The Remnant Group
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Sundermeyer, K. Symmetries in Fundamental Physics; Springer International Publishing: Berlin, Germany, 2014. [Google Scholar]
- Aldrovandi, R.; Pereira, J.G. Teleparallel Gravity; Springer: Dordrecht, The Netherlands, 2013; Volume 173. [Google Scholar]
- Ferraro, R.; Guzmán, M.J. Hamiltonian formulation of teleparallel gravity. Phys. Rev. D 2016, 94, 104095. [Google Scholar] [CrossRef]
- Ferraro, R.; Guzmán, M.J. Hamiltonian formalism for f(T) gravity. Phys. Rev. D 2018, 97, 104028. [Google Scholar] [CrossRef]
- Adak, M.; Sert, O. A Solution to symmetric teleparallel gravity. Turk. J. Phys. 2005, 29, 1–7. [Google Scholar]
- Adak, M.; Kalay, M.; Sert, O. Lagrange formulation of the symmetric teleparallel gravity. Int. J. Mod. Phys. D 2006, 15, 619–634. [Google Scholar] [CrossRef]
- Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, T. Coincident general relativity. Phys. Rev. D 2018, 98, 044048. [Google Scholar] [CrossRef] [Green Version]
- Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, T. The geometrical trinity of gravity. arXiv 2019, arXiv:1903.06830. [Google Scholar]
- Hayashi, K.; Shirafuji, T. New general relativity. Phys. Rev. D 1979, 19, 3524. [Google Scholar] [CrossRef]
- Ferraro, R.; Fiorini, F. Modified teleparallel gravity: Inflation without inflaton. Phys. Rev. D 2007, 75, 084031. [Google Scholar] [CrossRef]
- Bengochea, G.; Ferraro, R. Dark torsion as the cosmic speed up. Phys. Rev. D 2009, 79, 124019. [Google Scholar] [CrossRef]
- Cai, Y.F.; Capozziello, S.; De Laurentis, M.; Saridakis, E.N. f(T) teleparallel gravity and cosmology. Rep. Prog. Phys. 2016, 79, 106901. [Google Scholar] [CrossRef] [PubMed]
- Boehmer, C.G.; Fiorini, F. The regular black hole in four dimensional Born Infeld gravity. Class. Quant. Grav. 2019, 36, 12LT01. [Google Scholar] [CrossRef]
- Ferraro, R.; Guzmán, M.J. Quest for the extra degree of freedom in f(T) gravity. Phys. Rev. D 2019, 98, 124037. [Google Scholar] [CrossRef]
- Yang, R.J. Conformal transformation in f(T) theories. Eur. Phys. Lett. 2011, 93, 60001. [Google Scholar] [CrossRef]
- Wright, M. Conformal transformations in modified teleparallel theories of gravity revisited. Phys. Rev. D 2016, 93, 103002. [Google Scholar] [CrossRef] [Green Version]
- Chen, S.H.; Dent, J.B.; Dutta, S.; Saridakis, E.N. Cosmological perturbations in f(T) gravity. Phys. Rev. D 2011, 83, 023508. [Google Scholar] [CrossRef]
- Li, B.; Sotiriou, T.P.; Barrow, J.D. Large-scale structure in f(T) gravity. Phys. Rev. D 2011, 83, 104017. [Google Scholar] [CrossRef]
- Izumi, K.; Ong, Y.C. Cosmological perturbation in f(T) gravity revisited. J. Cosmol. Astropart. Phys. 2013, 1306, 029. [Google Scholar] [CrossRef]
- Golovnev, A.; Koivisto, T. Cosmological perturbations in modified teleparallel gravity models. J. Cosmol. Astropart. Phys. 2018, 1811, 012. [Google Scholar] [CrossRef]
- Ferraro, R.; Fiorini, F. Remnant group of local Lorentz transformations in f(T) theories. Phys. Rev. D 2015, 91, 064019. [Google Scholar] [CrossRef]
- Krššák, M.; Pereira, J.G. Spin Connection and Renormalization of Teleparallel Action. Eur. Phys. J. C 2015, 75, 519. [Google Scholar] [CrossRef]
- Krššák, M. Holographic renormalization in teleparallel gravity. Eur. Phys. J. C 2017, 77, 44. [Google Scholar] [CrossRef] [Green Version]
- Sotiriou, T.P.; Li, B.; Barrow, J.D. Generalizations of teleparallel gravity and local Lorentz symmetry. Phys. Rev. D 2011, 83, 104030. [Google Scholar] [CrossRef]
- Ong, Y.C.; Nester, J.M. Counting components in the lagrange multiplier formulation of teleparallel theories. Eur. Phys. J. C 2018, 78, 568. [Google Scholar] [CrossRef]
- Krššák, M.; Saridakis, E.N. The covariant formulation of f(T) gravity. Class. Quant. Grav. 2016, 33, 115009. [Google Scholar] [CrossRef]
- Golovnev, A.; Koivisto, T.; Sandstad, M. On the covariance of teleparallel gravity theories. Class. Quant. Grav. 2017, 34, 145013. [Google Scholar] [CrossRef]
- Hohmann, M.; Järv, L.; Krššák, M.; Pfeifer, C. Teleparallel theories of gravity as analogue of nonlinear electrodynamics. Phys. Rev. D 2018, 97, 104042. [Google Scholar] [CrossRef] [Green Version]
- Hohmann, M.; Järv, L.; Ualikhanova, U. Covariant formulation of scalar-torsion gravity. Phys. Rev. D 2018, 97, 104011. [Google Scholar] [CrossRef] [Green Version]
- Krššák, M.; Van Den Hoogen, R.J.; Pereira, J.G.; Boehmer, C.G.; Coley, A.A. Teleparallel theories of gravity: Illuminating a fully invariant approach. arXiv 2018, arXiv:1810.12932. [Google Scholar]
- Maluf, J.W.; Ulhoa, S.C.; da Rocha-Neto, J.F. Difficulties of Teleparallel Theories of gravity with local Lorentz symmetry. arXiv 2018, arXiv:1811.06876. [Google Scholar]
- Blixt, D.; Hohmann, M.; Pfeifer, C. Hamiltonian and primary constraints of new general relativity. Phys. Rev. D 2019, 99, 084025. [Google Scholar] [CrossRef] [Green Version]
- Hohmann, M.; Järv, L.; Krššák, M.; Pfeifer, C. Modified teleparallel theories of gravity in symmetric spacetimes. arXiv 2019, arXiv:1901.05472. [Google Scholar]
1 | Other authors define the affine connection as . |
2 | The anti-symmetry of the spin connection implies that , and . |
3 | Notice that the coefficients , are the links between anholonomous and coordinate basis. |
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Bejarano, C.; Ferraro, R.; Fiorini, F.; Guzmán, M.J. Reflections on the Covariance of Modified Teleparallel Theories of Gravity. Universe 2019, 5, 158. https://doi.org/10.3390/universe5060158
Bejarano C, Ferraro R, Fiorini F, Guzmán MJ. Reflections on the Covariance of Modified Teleparallel Theories of Gravity. Universe. 2019; 5(6):158. https://doi.org/10.3390/universe5060158
Chicago/Turabian StyleBejarano, Cecilia, Rafael Ferraro, Franco Fiorini, and María José Guzmán. 2019. "Reflections on the Covariance of Modified Teleparallel Theories of Gravity" Universe 5, no. 6: 158. https://doi.org/10.3390/universe5060158
APA StyleBejarano, C., Ferraro, R., Fiorini, F., & Guzmán, M. J. (2019). Reflections on the Covariance of Modified Teleparallel Theories of Gravity. Universe, 5(6), 158. https://doi.org/10.3390/universe5060158